UPDATE:
I haven't gone with blimp yet but am still considering it. But I did acquire a Seinnheiser 416 which I've connected to a Zoom F3 that's mounted on my Z's Tilta cage. I'm using a generic combo foam+dead cat on the mic that I got from Amazon which fits the 416. The 416 is held by Smallrig's shotgun mic holder mounted to a cold shoe on the Tilta cage and is connected to the the F3's channel 1 through an XLR cable. The F3 provides phantom power to the 416 from its 2 AA batteries. The mono signal is outputted from the F3 through the line-out to the Z9 using a regular TRS cable so the Z9 records the mono signal on both channels. I'm not recording on the F3 because I don't want any synching headaches. I realize I'm not getting the benefit of 32bit recording when connected this way, but not having the need for gain controls greatly simplifies things.
I used this setup for the first time yesterday shooting eagles. I need more experience but so far I really like what I'm hearing. The 416 is no replacement for a parabolic dish of course, but it's REALLY senstive and picks up everything, even very soft sounds when carefully walking around the tripod. But that's just fine -- bird calls can can be soft/faint so sensitivity is what I want. I was amazed when I got home and reviewed the recordings to hear some faint red-headed woodpecker calls in the distance that I did not hear when on site.
The only problem I've encountered is while I can use the F3's tone calibration function to set the recording levels on the Z9, when I switch to the 416 the signal drops drastically for some reason (seems to need a lot of gain), so I have to manually set (i.e. boost) the output levels on the F3 (currently 0db but may have to increase) to achieve acceptable recording levels on the Z9. Of course the Z9's attenuator must be turned off.
I'm going to test this setup before investigating the blimp option.
I'm also considering buying a parabolic dish to set on a tripod and plugging it in (or wirelessly connecting it) to the F3's second channel.